What is the absolute viscosity of the medium lubricating oil in N×s/m2?

In summary, the conversation discusses the calculation of the absolute viscosity of medium lubricating oil pumped through a 300m horizontal pipe with a diameter of 50mm and a flow rate of 0.00114 m^3/s. The pressure drop is given as 200 kPa and the specific gravity of the oil is 0.86. The conversation also mentions an equation for pressure drop in the laminar flow regime and the significance of the number 32 in the equation. The solution for the absolute viscosity is approximately 0.09 (N s)/m^2.
  • #1
archeryguru2000
2
0

Homework Statement


Medium lubricating oil, of specific gravity 0.860, is pumped through 300 m of horizontal 50-mm-diameter pipe at the rate of 0.00114 m3/s. If the drop in the pressure is 200 kPa, the absolute viscosity of the oil in N×s/m2 is...____________?

specific gravity (SG) = 0.86
length (l) = 300 m
diameter (d) = .05 m
flow rate (Q) = 0.00114 m^3/s
Pressure drop (P) = 200E3 Pa


Homework Equations


I know that:
shear stress (t) = viscosity (mu) * velocity gradient

where:
velocity gradient = (change in velocity) / (change in height)


The Attempt at a Solution



I'm not quite sure how to begin with this. I have a solution from my prof. (this is a question on a sample/practice exam for our final)... but I have NO clue where he's coming up with this equation:

P = 32 * (mu) & (l) * [(v)/(.05m)^2]

Where on Earth does the 32 come from? What significance does the (.05m)^2 have... without pi/4 anyway? Can anyone make any sense of this? The solution is supposed to be... approximately 0.09 (N s) / (m)^2. Let me know if anybody has any ideas.

Thanks,
~~Chad~~
 
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  • #2
You would have to check Reynolds number, but your prof references an equation for pressure drop in the laminar flow regime. You need to back through the proof for the equation, but the 32 comes from:

[tex]Q = \frac{\pi R^2 V_c}{2}[/tex]

[tex]V = \frac{\pi R^2 V_c}{2 \pi R^2}[/tex]

[tex]V = \frac{V_c}{2}[/tex]

Therefore

[tex]V = \frac{\Delta p D^2}{32 \mu L}[/tex]

In stead of going through the entire derivation, go here and look under the section "Volumetric Flow Rate."

http://www.ae.su.oz.au/aero/fprops/pipeflow/node7.html
 
Last edited:
  • #3
Thank you sooo much. This does clear up the issue with the "32" that I had a problem with.

Thanks,
~~Chad~~
 
  • #4
Glad to be of assistance archeryguru2000.
 

1. What is the role of viscosity in oil fluid mechanics?

Viscosity is a measure of a fluid's resistance to flow. In oil fluid mechanics, viscosity plays a crucial role in determining the rate at which oil flows through a system. High viscosity oils are thicker and flow slower, while low viscosity oils are thinner and flow faster. The viscosity of oil also affects its ability to lubricate and transfer heat.

2. How does temperature affect the fluid mechanics of oil?

Temperature has a significant impact on the fluid mechanics of oil. As temperature increases, the viscosity of oil decreases, making it flow faster. This phenomenon is known as thermal thinning. Additionally, high temperatures can also cause oil to break down and lose its lubricating properties, leading to increased friction and wear in machinery.

3. What is the difference between dynamic and kinematic viscosity?

Dynamic viscosity is a measure of a fluid's resistance to shear stress, while kinematic viscosity is a measure of a fluid's resistance to flow under the influence of gravity. In the context of oil fluid mechanics, dynamic viscosity is more relevant as it directly affects the rate of flow through a system. Kinematic viscosity is often used to characterize the behavior of oil in large-scale applications, such as pipelines.

4. How is oil pressure affected by fluid mechanics?

In fluid mechanics, pressure is defined as the force exerted by a fluid per unit area. In the case of oil, pressure is affected by factors such as viscosity, density, and flow rate. Higher viscosity oils will experience higher pressure drops as they flow through a system. Additionally, changes in flow rate and fluid density can also impact oil pressure.

5. What are some common applications of oil fluid mechanics?

Oil fluid mechanics is used in a wide range of applications, including lubrication of machinery, hydraulic systems, and transportation of oil in pipelines. It is also essential in the design and operation of oil drilling and production systems. Additionally, understanding oil fluid mechanics is crucial for the proper maintenance and performance of engines and other mechanical systems that rely on oil for lubrication and cooling.

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